April 2017
Problem of the Month

College Math

Can you rank the college logos from the 10 clues below?
Each logo has a value from 1 to 10, and no two logos have the same value.

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Give the answer for each of the following logos:

	Arkansas Razorbacks =
	Baylor Bears =
	Clemson Tigers =
	Colorado State Rams =
	Hartwick Hawks =
	James madison Dukes =
	Richmond Spiders =
	Wake Forest Demon Deacons =
	William & Mary Tribe =
	Wyoming Cowboys =

Click here for a printer version of this puzzle

Solution to the Problem:

The Top Ten College logos are:
1. Clemson Tigers
2. Baylor Bears
3. Wake Forest Demon Deacons
4. James Madison Dukes
5. William & Mary Tribe
6. Colorado State Rams
7. Hartwick Hawks
8. Arkansas Razorbacks
9. Richmond Spiders
10. Wyoming Cowboys

To solve the puzzle, let A = William & Mary, B = Richmond, C = Wyoming, D = Clemson
E = Wake Forest, F = Arkansas, G = Colorado State, H = Baylor, I = James Madison, J = Hartwick

Then you can write the following ten equations:
(1)   D + B = 10
(2)   A + C = 5 * E
(3)   H + B = E + F
(4)   A + J = E + B
(5)   B = A + I
(6)   C = F + H
(7)   G = H + E + 1
(8)   G + E = H + 7
(9)   G + H = E + 5
(10)   A + I + F = 17

Begin with equations 7, 8, and 9 to solve for G, H, and E.
Substitute equation 7 in both equation 8 and equation 9:
H + E + E + 1 = H + 7   =>   2E = 6   =>   E = 3
H + E + 1 + H = E + 5   =>   2H = 4   =>   H = 2
Then G = 2 + 3 + 1 = 6

Now substitute the values for G, E, and H in the other equations above.

A + C = 15
B = 1 + F
A + J = 3 + B
C = F + 2

So B = A + J - 3
A = 15 - F - 2
A = 1 + F - I
A = 13 - F
13 - F = 1 + F - I
I = 2F - 12

A + F + I = 17
13 - F + F + 2F - 12 = 17
So, F = 8

Now, A = 5 and I = 4

Then B = 1 + 8 = 9 and D = 1.

C = 8 + 2 = 10 (from equation 6)
5 + J = 3 + 9 so J = 7 from equation 4.

Correctly solved by:

1. Eliza Sheffield and Anna Vice	Tuscaloosa, Alabama
2. James Cotter	Baylor University, Waco, Texas
3. Keylee Esplin	Delta High School, Delta, Colorado
4. Tyler Stoddard	Mountain View High School, Mountain View, Wyoming
5. Ivy Joseph	Pune, Maharashtra, India
6. Christian Elsborg	Mountain View High School, Mountain View, Wyoming
7. Cooper Martin	Mountain View High School, Mountain View, Wyoming
8. Madison Bindl	Mountain View High School, Mountain View, Wyoming
9. Brijesh Dave	Mumbai city, Maharashtra, India
10. Tyson Roberts	Mountain View High School, Mountain View, Wyoming
11. Cailee Hamilton	Mountain View High School, Mountain View, Wyoming
12. Raegan Martin	Mountain View High School, Mountain View, Wyoming
13. Oceana Bergholtz	Delta High School, Delta, Colorado
14. Linzy Carpenter	----------
15. Trevon Peterson	Mountain View High School, Mountain View, Wyoming
16. Behlee Aimone	Mountain View High School, Mountain View, Wyoming
17. Valerie Walker	----------
18. Sabre Williams	----------
19. Karlee Hereford	Mountain View High School, Mountain View, Wyoming
20. Skyler Kraai	Delta High School, Delta, Colorado
21. Sami Lane	Delta High School, Delta, Colorado
22. Sameha Haque	Delta High School, Delta Colorado
23. Miko Zhang	Delta High School, Delta, Colorado
24. Ben Todd	Mountain View High School, Mountain View, Wyoming
25. Sierra Toomer	Mountain View High School, Mountain View, Wyoming
26. Jaden Downey	Mountain View High School, Mountain View, Wyoming
27. Caden Stoll	Mountain View High School, Mountain View, Wyoming
28. Kelsey Giorgis	Mountain View High School, Mountain View, Wyoming
29. Claire Corbasson	Mountain View High School, Mountain View, Wyoming
30. Nate Moretti	Mountain View High School, Mountain View, Wyoming
31. Dawson Case	Mountain View High School, Mountain View, Wyoming
32. Christopher Woody	Mountain View High School, Mountain View, Wyoming
33. Baylee Tims	Mountain View High School, Mountain View, Wyoming
34. Austin Smith	Mountain View High School, Mountain View, Wyoming
35. Tom Moschner	Pasco County Schools New Port Richey, Florida
36. Brianna Tims	Mountain View High School, Mountain View, Wyoming
37. Deloss Hancock	Delta High School, Delta, Colorado
38. Hunter Gross	Mountain View High School, Mountain View, Wyoming
39. Adalene Thomas	Mountain View High School, Mountain View, Wyoming
40. Faith Pfeifer	Mountain View High School, Mountain View, Wyoming
41. Hope Pfeifer	Mountain View High School, Mountain View, Wyoming
42. Harlan Benedict	Mountain View High School, Mountain View, Wyoming
43. Jason Stoddard	Mountain View High School, Mountain View, Wyoming
44. Kenzy Kellum	Mountain View High School, Mountain View, Wyoming
45. Makell Kaiser	Mountain View High School, Mountain View, Wyoming
46. Kylie Walker	Mountain View High School, Mountain View, Wyoming
47. Braeden Walk	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher